What time period in history does Thing Fall Apart take place? What is a major event that happened around this time?

The influx of Christianity into the villages more in the interior of Africa is likely the best clue as to the time period, indicating that it is likely sometime around the late 1800s as that was the time that the majority of missionaries arrived and began to establish Christian outposts in many of the villages.

If you look in the book, it is in the second part of the book, around chapters 16-25 that the Christian church is built after they obtain a piece of land in the forbidden forest and begin to convert villagers and build up a presence in the village.

Historically they began to run the school system and found this to be another effective way to undermine the Ibo culture and strengthen their own influence.